Question

1/64, 1/16, 1/4, 1... What is the pattern and next term???

Answer 1

`\huge\boxed{\text{next term}=4}\\\boxed{f(n)=4^(n-4)}`

Explanation:

`(1)/(64),\ (1)/(16),\ (1)/(4),\ 1,\ ...`

It's the geometric sequence where

`a_1=(1)/(64),\ q=4`

`(1)/(16)=(1)/(64)\cdot4\\\\(1)/(4)=(1)/(16)\cdot4\\\\1=(1)/(4)\cdot4\\\\1\cdot4=4\to\text{next term}`

`f(n)=(1)/(64)\cdot4^(n-1)=(1)/(4^3)\cdot4^(n-1)=(4^(n-1))/(4^3)\\\\\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\f(n)=4^(n-1-3)=4^(n-4)`